Given the inverse demand function p = 100 - 20q for toasters and a price of $35, we can find the consumer surplus.
First, we'll find the quantity demanded at the given price:
35 = 100 - 20q
20q = 100 - 35
q = (100 - 35) / 20
q = 65 / 20
q = 3.25
Now, to find the consumer surplus, we'll use the formula:
Consumer Surplus = (1/2) × Base × Height
The base represents the quantity (q = 3.25) and the height is the difference between the maximum willingness to pay (p = 100) and the actual price (p = 35).
Consumer Surplus = (1/2) × 3.25 × (100 - 35)
Consumer Surplus = 0.5 × 3.25 × 65
Consumer Surplus = 105.625
So, the consumer surplus is $105.63 when rounded to two decimal places.
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HELP PLEASE I NEED THIS DONE ASAP
Answer:5
Step-by-step explanation:
it would be 5 because
4. Find the area of the shaded region. 5 ft 9 ft 3 ft 4 ft A. 36 ft² B. 38 ft² C. 39 ft² D. 40 ft²
Due before 8:30
Answer:
C. 39 ft²
Step-by-step explanation:
Area of the outer rectangle which includes the white triangle
= length x width
= 5 x 9
= 45 ft²
Area of the white triangle
= 1/2 x base x height
= 1/2 x 4 x 3
= 6 ft²
Area of shaded region
= Area of rectangle - Area of triangle
= 45 - 6
= 39 ft²
The proportion of scores in a standard Normal Distribution that are greater than 1.25 is closest to...a) .1056b) .1151c) .1600d) .8849e) .8944
The proportion of scores in a standard Normal Distribution that are greater than 1.25 is closest to a. a is 0.1056.
The proportion of scores in a standard Normal Distribution that are greater than 1.25 is:
[tex]P(Z > 1.25) = 1 - P(Z < 1.25)[/tex]
Using a standard normal distribution table or a calculator.
The area to the left of 1.25 is 0.8944, so:
[tex]P(Z > 1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056[/tex]
The closest answer choice is (a) 0.1056.
The percentage of scores in a normal distribution with a standard deviation larger than 1.25 is:
either a calculator or a normal distribution standard table.
0.8944 is the region to the left of 1.25, so:
The nearest possible response is (a) 0.1056.
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A car has 12,500 miles on its odometer. Say the car is driven an average of 40 miles per day. Choose the model that expresses the number of miles N that will be on its odometer after x days Choose the correct answer below ( A. N(x)=12.500x + 40 OB. N(x)--40x + 12,500 OC. Nx)-40-12,500 O D. N(x)-40x+12,500
The correct answer is B.
N(x) = 40x + 12,500.
This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.
Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.
Based on the given information, the correct answer is B.
N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.
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The correct answer is B.N(x) = 40x + 12,500.
This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.
Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.
Based on the given information, the correct answer is B.
N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.
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HELP I GOT AN F IN MATH AND MY MOMMA AINT GONNA LIKE IT WHEN SHE FINDS OUT
The quadratic equation y = x²-6x+5 is minimum because the coefficient of x² is positive.
x = [tex]\frac{-b}{2a}[/tex], but a = 1 and b = -6
therefore x = [tex]\frac{-(-6)}{2(1)}[/tex] = 3
By plugging the value in the quadratic equation above, then we have
y = (3)² - 6(3) + 5 = -4 = -4
Note that y is the y-value of the vertex.
How to determine the minimum/maximum of a functionTo determine whether the function y = x^2 - 6x + 5 has a maximum or minimum value, we can use the vertex formula, which gives the x-coordinate of the vertex of a quadratic function as -b/2a.
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Choose a Strategy. Ms. Jimenez earns $27,000 per year. She is paid weekly. She puts 8% of her salary in a retirement fund. How much money goes into this fund each week?
After answering the presented question, we may conclude that expressions As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
We need to do the following to figure out how much money Ms. Jimenez puts into her retirement fund each week:
Ms. Jimenez's yearly retirement fund contribution is calculated as follows:
8% of $27,000 = annual retirement fund contribution
= 0.08 x $27,000
= $2,160
To calculate the weekly retirement fund contribution, divide the yearly payment by the number of weeks in the year:
Contribution to a retirement fund on a weekly basis = Annual contribution to a retirement fund divided by the number of weeks in a year
= $2,160 / 52
≈ $41.54
As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.
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Solve for A and B using special right triangles
Answer:
a = 10
b = 5
Step-by-step explanation:
A 30-60-90 triangle is a right triangle where the interior angles measure 30°, 60° and 90° and the sides are in the ratio 1 : √3 : 2.
The formula for the ratio of the sides is x : x√3 : 2x where:
x = the shortest side opposite the 30° angle.x√3 = the side opposite the 60° angle.2x = the longest side (hypotenuse) opposite the right angle.From inspection of the given triangle, the measure of the side opposite the 30° angle is "b", the side opposite the 60° angle is 5√3, and the hypotenuse is "a". Therefore:
x = bx√3 = 5√3 2x = aIf x√3 = 5√3, then x = 5. Therefore:
b = x = 5a = 2x = 10What is the most common type of employee benefit?
O retirement
O disability insurance
O life insurance
O healthcare
Answer:
life insurance is the most common type of employee benefit
The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides.
5,2.2360679775,5.47722557505
On solving the provided question we can say that As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle.
what is Pythagorean theorem?The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.
The supplied figures reflect the lengths of the three sides of a right triangle, with the hypotenuse (the side opposite the right angle) being 5.47722557505, and the other two sides being 2.2360679775 and 5.
The sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, according to the Pythagorean theorem. In this situation, we can write:
2.2360679775² + 5² = 5.47722557505²
When we simplify and solve for one of the variables, we get:
5² = 5.47722557505² - 2.2360679775²
25 = 24.9999999999971
As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle. We could round the data to approach the sides of a right triangle, but it would not get accurate solutions.
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explain each step in the process of finding the area of a circle given the circumfrence
Answer:
Divide the circumference by [tex]2\pi[/tex]Square the remaining numberMultiply the resulting value by [tex]\pi[/tex]Step-by-step explanation:
Recall that the formula for the circumference of a circle is:
[tex]2\pi r[/tex]
Also recall that the formula for the area of a circle is:
[tex]\pi r^2[/tex]
Both formulas use the radius; one squares it, while the other doubles it.
Let's start by turning the formula for the circumference of a circle into the formula for the area of a circle. We start off with:
[tex]2\pi r[/tex]
We want to square the radius, but we can't do that without squaring everything else, too, so let's get rid of the other terms.
Divide the circumference by [tex]2\pi[/tex]:
[tex]2\pi r\\\frac{2\pi r}{2\pi } =\\r[/tex]
Now, we can square r:
[tex]r\\r^2[/tex]
Now, all we have to do is multiply by pi:
[tex]r^2\\\pi r^2[/tex]
We now have the area.
Let's look back at out steps.
First, we divided the circumference by [tex]2\pi[/tex].
Next, we squared the number we had left (the radius).
Finally, we multiplied by [tex]\pi[/tex].
o determine whether voters would be willing to vote for a tax increase to improve the city's parks, the park commission surveys 500 park users.
Why is this sample likely to be biased?
This sample is likely to be biased because it only includes individuals who use the city's parks, which means it may not represent the entire population of voters who would be affected by a tax increase to improve the parks.
What is sample?A sample is a subset or a smaller group of individuals or 17 that are selected from a larger population to represent the population.
According to question:The park commission's study of 500 park users is likely biassed because it only covers people who use the city's parks. This indicates that the sample does not accurately reflect the full electorate who would be impacted by a tax hike to fund park improvements.
Various people may hold various views regarding whether or not a tax increase is required to develop the parks. For instance, if they don't frequent the parks or have other priorities for their tax money, they might be less likely to approve a tax hike.
If the park commission only conducted surveys of people at specific times of day or in specific locations of the city, the sample may also be skewed. This could omit those who visit the parks at various hours or in various locations around the city.
In order to get accurate and valid results, it's crucial to utilise a representative sample that includes people from different demographic groups. A biased sample can produce results that are erroneous or misleading.
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The time $t$t (in seconds) it takes a dropped object to fall h$h$h feet is given by t is equal to square root of h over 16 end root$t=\sqrt{\frac{h}{16}}$t=√
h
16 .
A building of height 55 feet.
a. Estimate how long it takes an earring to hit the ground when it falls from the roof of the building. Round your answer to the nearest hundredth.
about ____ seconds
b. Estimate how much sooner the earring hits the ground when it is dropped from two stories (22 feet) below the roof. Round your answer to the nearest hundredth.
about seconds
Kyle who is a lifeguard is roping off a rectangular swimming area of 70 m. He uses the beach as one side.
Determine the minimum length, to 2 decimal places, of rope needed.
If he uses the beach as one side. the minimum length, to 2 decimal places, of rope needed is: 70 meters of rope.
What is the minimum length?Let's assume that the length of the swimming area is L and the width is W. The perimeter of the swimming area will be the length of the rope that Kyle needs to rope off the area.
From the problem, we know that one side of the swimming area is the beach, so we have:
L + W + L = 70
Simplifying this equation, we get:
2L + W = 70
To find the minimum length of rope needed, we need to minimize the perimeter of the swimming area. We can use the above equation to express W in terms of L:
W = 70 - 2L
Substituting this expression for W into the formula for the perimeter, we get:
P = L + W + L
= 2L + (70 - 2L)
= 70
So the perimeter of the swimming area is fixed at 70 m, regardless of the values of L and W. Therefore, the minimum length of rope needed to rope off the area is simply the perimeter of the swimming area, which is 70 meters.
Therefore, Kyle needs a minimum of 70 meters of rope.
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Where will the parabola intersect the line? What equation did you solve to find the intersection? Question content area bottom
Part 1 Use the equation to find the intersection.
The parabola will intersect the line at____enter your response here.
From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).
What is a parabola and how do we obtain the equations of the same?A parabola is a type of curve that can be described as a symmetrical U-shape. The generalized equation of a parabola is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are constant values.This equation represents a vertical parabola with its vertex at the point [tex](-b/2a, c - b^2/4a)[/tex] and an axis of symmetry that is parallel to the y-axis.This equation represents a parabola that opens to the right or left, with its vertex at the point [tex](c - b^2/4a, -b/2a)[/tex] and an axis of symmetry that is parallel to the x-axis. The specific coefficients in the equation depend on the particular characteristics of the parabola, such as its vertex, axis of symmetry, and whether it opens up or down or left or right.As the parabola is originating from the origin and opens at the y-axis, hence:
Equation of parabola = [tex]x^{2} =4ay[/tex] {where a =2} .....................(1)Equation of the line=[tex]y-7=0[/tex].............................................(2)From equation 2 we obtain y=7 and will put this value in 1.After computing the above values in 1 we get: [tex]x^{2} =4*2*7\\x=\sqrt{4*2*7}\\ x=2\sqrt{14}[/tex] and y=7So the coordinates at which the parabola intersects the line is [tex](2\sqrt{14} ,7)[/tex]To know more about the parabola visit:
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A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 6
Spade 4
Club 7
Diamond 3
Determine the experimental probability of drawing a spade.
0.15
0.20
0.40
0.45
The experimental probability of drawing a spade is 0.2
How to determine the experimental probability?When we perform an experiment N times, and we got a given outcome K times, the experimental probability of said outcome is given by the quotient:
P = K/N
Here the experiment is performed:
N = 6 + 4 + 7 + 3 = 20 times
And a spade is drawn 4 times, then the experimental probability is:
P = 4/20 = 1/5 = 0.20
The correct option is the second one.
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A rhombus has a diagonals of 6 inches and 8 inches. what is the perimeter and the area of the rhombus?
the perimeter of the rhombus is 20 inches, and the area is 24 square inches.
How to solve the question?
To find the perimeter of a rhombus, we need to know the length of one side. Fortunately, we can use the properties of a rhombus to find the length of the sides. A rhombus has two pairs of equal-length sides, so we can use the Pythagorean theorem to find the length of each side.
Let's label the diagonals of the rhombus as d1 and d2. The diagonals of a rhombus bisect each other at right angles, so we can draw a right triangle with half of each diagonal as the legs and a side of the rhombus as the hypotenuse. Using the Pythagorean theorem, we can find the length of the sides:
(1/2)d1 = 3 inches
(1/2)d2 = 4 inches
Side length = √((1/2)d1² + (1/2)d2²) = √(9 + 16) = 5 inches
Now that we know the length of the sides, we can find the perimeter:
Perimeter = 4 x side length = 4 x 5 = 20 inches
To find the area of the rhombus, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
Area = (6 x 8) / 2 = 24 square inches
So the perimeter of the rhombus is 20 inches, and the area is 24 square inches.
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A rectangle is 5√7+2√3 meters long and 6√7-3√3 meters wide.
a. Find the perimeter of the rectangle in simplest form.
b. Find the area of the rectanglè in simplest form
The a. Perimeter = 22√7 - 2√3 meters. The Area = 4√12 - 3√7 square meters
How to Find the Area and Perimeter of a Rectangle?Area = length * width
Perimeter = 2(length + width)
Given the following:
Length of the rectangle = 5√7 + 2√3 meters
Width of the rectangle = 6√7 - 3√3 meters
a. Perimeter = 2(5√7 + 2√3) + 2(6√7 - 3√3)
10√7 + 4√3 + 12√7 - 6√3
22√7 - 2√3 meters
b. Area = (5√7 + 2√3)(6√7 - 3√3)
= 5√7(6√7 - 3√3) + 2√3(6√7 - 3√3)
= 210 - 15√21 + 12√21 - 18
= 192 - 3√7
= 4√12 - 3√7 square meters
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Given that ZQRP = (2x + 20) and ZPSQ = 30°, find the value of x.
The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.
We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.
If angles QRP and PSQ are supplementary, their sum is 180°:
(2x + 20)° + 30° = 180°
Now, we can solve for x:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide by 2:
x = 65
can someone help me w this
Find the surface area of the composite solid.
The surface area of the figure is derived to be equal to 656.4 square meters.
How to evaluate the surface area of a cylinderThe top of the figure is a triangular prism, the bottom is a triangle, and the sides are 3 same size rectangles, so the surface area is calculated as follows:
area of one top triangle face = 1/2 × 12 m × 5 m = 30 m²
area of top triangular prism = 3 × 30 m² = 90 m².
area of bottom triangle = 1/2 × 12 m × 10.4 m = 62.4 m²
area of one rectangle side = 14 m × 12 m = 168 m²
area of the three rectangle sides = 3 × 168 m² = 504 m²
surface area of the figure = 90 m² + 62.4 m² + 504 m²
surface area of the figure = 656.4 m².
Therefore, the surface area of the figure is derived to be equal to 656.4 square meters.
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Alvin's new bag of 50 marbles of different
designs spilled in his backpack. On the way
home from school, he randomly selects one
marble from the backpack, records the
result, puts the marble back in the bag,
and selects again. Here are his results:
jasper, galaxy, cat's-eye, rainbow,
galaxy, sunburst, galaxy, cat's-eye,
sunburst, jasper
Based on the data, estimate how many of
the marbles in Alvin's backpack are galaxy
marbles.
If necessary, round your answer to the
nearest whole number.
Answer: 7
Step-by-step explanation:
i did it a weird way
Please help me I can also offer a commission too
The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:
f(x): -1.25.g(x): -0.715.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), we have that:
When x = 2, y = 7.When x = 6, y = 2.Hence the rate is given as follows:
r = (2 - 7)/(6 - 2)
r = -5/4
r = -1.25.
For the function g(x), we have that:
When x = 2, y = 2(-5/7) - 6 = -7.43.When x = 6, y = 6(-5/7) - 6 = -10.29.Hence the rate is given as follows:
r = (-10.29 - (-7.43))/(6 - 2)
r = -0.715
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What is the value of x in the right triangle below?
Show your work and round your answer to the nearest hundredth.
The value of x in the right triangle below by using Pythagorean Theorem (H² = P² + B²) is 19.53
According to question; Perpendicular (P) = 16, Base (B) = 11.2 and Hypoteneus (H) = X
According to Pythagorean Theorem
H² = P² + B²
X² = 16² + 11.2²
X² = 256 + 125.44
X² = 381.44
X = 19.53
The Pythagorean Theorem is what?The Pythagorean Theorem, or, in standard algebraic notation, a² + b² = c², states that the total of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).
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11. Tyrell buys an organizer for his baseball cards that costs $12.99. He can
add pages to the organizer to hold the cards. Each page costs $2.75 and
holds 9 cards. If Tyrell has 100 cards, how much will it cost him to organize
them? Write and evaluate a numeric expression.
On solving the provided question we can say that - 12.99(y - 9) + 2.75y = 100 , by solving, the expression x = 11.2, y = 19
What is linear equation?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
let x be the base ball cards.
and y be page card.
x + y = 9 -------------------1
12.99x + 2.75y = 100-------------------2
12.99(y - 9) + 2.75y = 100
by solving
x = 11.2
y = 19
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The given equation shows a proportional relationship betweenthe variables r and s. Which expression is equivalent to 6r. R=10/3s
The equivalent expression for 6r in terms of s is 20s, which we obtain by substituting the value of r from the given equation and simplifying.
The given equation, r = (10/3)s, shows that there is a proportional relationship between the variables r and s. This means that when one variable changes, the other variable changes in direct proportion to it. In other words, if we increase r by a certain factor, s will increase by the same factor, and vice versa.
To find an expression that is equivalent to 6r, we can substitute the value of r from the given equation and simplify.
r = (10/3)s (given equation)
6r = 6(10/3)s (substitute 6r for r in the equation)
6r = 20s (simplify by multiplying 6 and 10/3)
Therefore, the expression that is equivalent to 6r in terms of s is 20s. This means that if we know the value of s, we can use this expression to find the value of 6r in a proportional relationship. For example, if s = 2, then 6r = 20s = 20(2) = 40.
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smo help me fill in the charts, will give brainliest
Answer:
In the explanation
Hope this helps!
Step-by-step explanation:
a.
1. LCM of 2 & 5 is 10
2. [tex]\frac{15x}{10} =\frac{12}{10}[/tex] -> 15x = 12
3. x = [tex]\frac{12}{15}[/tex] or [tex]\frac{4}{5}[/tex]
b.
1. LCM of 3 & 9 is 9
2. 2x - [tex]\frac{6}{9}[/tex] = [tex]\frac{4}{9}[/tex] -> 2x = [tex]\frac{10}{9}[/tex] -> [tex]\frac{18}{9} x[/tex] = [tex]\frac{10}{9}[/tex] -> x = [tex]\frac{10}{9}[/tex] × [tex]\frac{9}{18}[/tex] -> x = [tex]\frac{10}{18}[/tex] -> x = [tex]\frac{5}{9}[/tex]
3. x = [tex]\frac{5}{9}[/tex]
Find a possible solution to the equation cos(x+2)=sin(3x)
A.
x=0. 5 degrees
B.
x=1 degree
C.
x=22 degrees
D.
x=44 degrees
A possible solution to the equation cos(x+2)=sin(3x) is x = 22 degrees
The correct answer is an option (C)
Consider a trigonometric equation,
cos(x+2) = sin(3x)
For value x = 0.5 degrees,
cos(x + 2) = cos(2.5)
= 0.999
and sin(3x) = sin(1.5)
= 0.026
For x = 1 degree,
cos(x + 2) = cos(3)
=0.9986
sin(3x) = sin(3)
= 0.052
For x = 22 degrees
cos(x + 2) = cos(24)
= 0.913
sin(3x) = sin(66)
= 0.913
for x = 44 degrees,
cos(x + 2) = cos(46)
= 0.69
sin(3x) = sin(132)
= 0.743
Therefore, the solution to an equation cos(x+2) = sin(3x) is x = 22 degrees
The correct answer is an option (C)
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2. Find the volume. Show work, and round to 2 decimal places
*triangle based prism*
answer
as we all know volume is equal to length times width times height therefore to get you answer you have to multiply all the three giving measurements the answer that you get you are supposed to round it to the nearest to decimal places when you say around it off to the nearest two decimal places it means that they need to be too this two numbers after the coma
why does an angle formed by a tngent and a chord have the same measure as an insribed angle that intercepts the same arc
An angle formed by a tangent and a chord in a circle is called an "angle between tangent and chord" while an inscribed angle is an angle whose vertex is on the circle and whose sides intersect the circle at two distinct points.
When a tangent line and a chord intersect at a point on the circle, the tangent line is perpendicular to the radius drawn to the point of intersection.
This means that the angle between the tangent and the chord is equal to the angle between the radius and the chord.
Now, consider an inscribed angle that intercepts the same arc as the chord.
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that it intercepts.
Thus, the measure of the inscribed angle is equal to the measure of the arc that the chord intercepts.
Since the angle between the tangent and the chord is equal to the angle between the radius and the chord, and the inscribed angle intercepts the same arc as the chord, it follows that the angle between the tangent and the chord is equal to the inscribed angle that intercepts the same arc.
Therefore, an angle formed by a tangent and a chord has the same measure as an inscribed angle that intercepts the same arc.
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Michelle was instructed to write two equivalent expressions for 6x + 15.
Her work is shown.
6x + 15 = x + x + x + x + x + x + 15
6x + 15 = 6(x + 15)
Part A: Explain which one of Michelle’s equations is true for all values of x and which one of Michelle’s equations is false for all values of x. (2 pts.)
Part B: Write another equivalent expression for 6x + 15.
Michelle’s equations that is true for all values of x is 6x + 15 = x + x + x + x + x + x + 15.
Michelle’s equations that is false for all values of x is 6x + 15 = 6(x + 15).
Another equivalent expression for 6x + 15 is 3(2x + 5).
What is an expression?In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).
Michelle’s equations can be written for all values of x as follows;
6x + 15 = x + x + x + x + x + x + 15.
However, Michelle’s equations is false for all values of x when it is written as 6(x + 15).
Another equivalent expression is given by;
6x + 15 = 3(2x + 5).
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Answer:
Part A: The equation 6x + 15 = 6(x + 15) is true for all values of x because it distributes the 6 to both terms inside the parentheses and simplifies to the original expression. However, the equation 6x + 15 = x + x + x + x + x + x + 15 is false for all values of x. While it may be true for specific values of x, such as x = 1 or x = 2, it is not true for all values of x because the number of x terms changes depending on the value of x.
Part B: Another equivalent expression for 6x + 15 could be 3(2x + 5), which also simplifies to the original expression. This is because we can factor out a common factor of 3 from both terms and simplify to 3(2x + 5) = 6x + 15.
Step-by-step explanation: